We report a 29Si-NMR study on the pressure-induced superconductivity (SC) in an antiferromagnetic (AFM) heavy-fermion compound CeIrSi3 without inversion symmetry. In the SC state at P=2.7-2.8 GPa, the temperature dependence of the nuclear-spin lattice relaxation rate 1/T_1 below Tc exhibits a T^3 behavior without any coherence peak just below Tc, revealing the presence of line nodes in the SC gap. In the normal state, 1/T_1 follows a sqrt{T}-like behavior, suggesting that the SC emerges under the non-Fermi liquid state dominated by AFM spin fluctuations enhanced around quantum critical point (QCP). The reason why the maximum Tc in CeIrSi3 is relatively high among the Ce-based heavy-fermion superconductors may be the existence of the strong AFM spin fluctuations. We discuss the comparison with the other Ce-based heavy-fermion superconductors.
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